Subgroups — C₁₁×#17875 #14595068

Order 2816.

698 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#2975	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1588	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1586	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1583	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1581	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1565	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic
13	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
15	C₈×Q₈×C₁₁	C₂²	1	2	yes	complemented
16	C₁₁×#442	C₄	1	2	yes	—
17	C₁₁×#440	C₄	1	2	yes	—
18	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
19	C₄×C₁₁×D₈	C₂²	1	2	yes	—
20	C₁₁×#436	—	2	1	no	—
21	C₁₁×#436	—	2	1	no	—
22	C₁₁×#436	C₂²	1	2	yes	—
23	C₁₁×#436	C₂²	1	2	yes	—
24	C₈×D₄×C₁₁	—	2	2	no	—
25	C₈×D₄×C₁₁	C₂²	1	2	yes	complemented
26	C₁₁×#431	—	2	1	no	—
27	C₁₁×#431	C₂²	1	1	yes	characteristic
28	C₁₁×#431	C₂²	1	1	yes	characteristic
29	C₁₁×#428	C₄	1	1	yes	characteristic
30	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
31	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₁₁×#418	C₄	1	1	yes	characteristic
33	C₁₁×#417	C₄	1	1	yes	characteristic
34	C₁₁×#407	—	2	2	no	—
35	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
37	C₁₁×#335	C₂²	1	2	yes	complemented
38	C₁₁×#334	C₂²	1	2	yes	complemented
39	C₁₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₁₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₁₁×D₄⋊C₈	C₂²	1	2	yes	—
42	C₁₁×D₄⋊C₈	C₂²	1	2	yes	—
43	C₁₁×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	C₁₁×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	C₁₁×#322	C₂²	1	2	yes	complemented
46	C₁₁×#322	C₂²	1	2	yes	complemented
47	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
48	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₁	—	2	1	no	—
50	C₁₁×AGL(1,ℤ/8)	—	2	4	no	—
51	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
53	C₂×C₁₁×M₁₆	—	2	2	no	—
54	C₂×C₁₁×M₁₆	—	2	2	no	—
55	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
56	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	—	2	1	no	—
58	C₂²×C₈×C₁₁	—	2	1	no	—
59	C₂²×C₈×C₁₁	—	2	2	no	—
60	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₁₁	—	2	1	no	—
63	C₄×D₄×C₁₁	—	2	1	no	—
64	C₄×D₄×C₁₁	—	2	1	no	—
65	C₄×D₄×C₁₁	—	2	1	no	—
66	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
67	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
68	C₄×D₄×C₁₁	C₂³	1	2	yes	—
69	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
70	C₁₁×#117	—	2	1	no	—
71	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₄²×C₁₁	—	2	1	no	—
75	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
76	C₁₁×#107	C₂×C₄	1	2	yes	—
77	C₁₁×#106	C₂×C₄	1	2	yes	—
78	C₁₁×C₄⋊C₈	—	2	2	no	—
79	C₁₁×C₄⋊C₈	—	2	1	no	—
80	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
81	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
83	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₁₁×#103	C₂×C₄	1	2	yes	—
86	C₁₁×#102	C₂×C₄	1	2	yes	—
87	C₁₁×#102	C₂×C₄	1	2	yes	—
88	C₁₁×#102	C₂×C₄	1	2	yes	—
89	C₁₁×C₂²⋊C₈	—	2	1	no	—
90	C₁₁×C₂²⋊C₈	—	2	2	no	—
91	C₁₁×C₂²⋊C₈	—	2	2	no	—
92	C₁₁×C₂²⋊C₈	—	2	2	no	—
93	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
94	C₁₁×#97	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₁₁	—	2	2	no	—
96	C₄×C₈×C₁₁	—	2	1	no	—
97	C₄×C₈×C₁₁	—	2	1	no	—
98	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₁	C₂³	1	2	yes	—
101	C₄×C₈×C₁₁	C₂³	1	2	yes	—
102	#17875	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₁	—	2	1	no	—
104	C₁₁×#41	—	2	2	no	—
105	C₁₁×#41	M₁₆	1	4	yes	complemented
106	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₂×D₄×C₁₁	—	2	1	no	—
108	C₂×D₄×C₁₁	—	2	1	no	—
109	C₂×D₄×C₁₁	—	2	2	no	—
110	C₂×D₄×C₁₁	—	2	2	no	—
111	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₁	—	2	1	no	—
114	C₂²×C₄×C₁₁	—	2	1	no	—
115	C₂²×C₄×C₁₁	—	2	1	no	—
116	C₂²×C₄×C₁₁	—	2	2	no	—
117	C₂²×C₄×C₁₁	—	2	1	no	—
118	C₂²×C₄×C₁₁	—	2	2	no	—
119	C₂²×C₄×C₁₁	—	8	1	no	—
120	C₂²×C₄×C₁₁	—	8	1	no	—
121	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
124	C₁₁×SD₁₆	—	2	4	no	—
125	C₁₁×D₈	—	2	4	no	—
126	C₁₁×M₁₆	—	2	2	no	—
127	C₁₁×M₁₆	—	2	2	no	—
128	C₁₁×M₁₆	—	8	2	no	—
129	C₁₁×M₁₆	—	8	2	no	—
130	C₂×C₈×C₁₁	—	2	1	no	—
131	C₂×C₈×C₁₁	—	2	1	no	—
132	C₂×C₈×C₁₁	—	2	2	no	—
133	C₂×C₈×C₁₁	—	2	1	no	—
134	C₂×C₈×C₁₁	—	2	1	no	—
135	C₂×C₈×C₁₁	—	4	2	no	—
136	C₂×C₈×C₁₁	—	8	1	no	—
137	C₂×C₈×C₁₁	—	8	2	no	—
138	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
140	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
142	C₁₁×C₄⋊C₄	—	2	1	no	—
143	C₁₁×C₄⋊C₄	—	2	1	no	—
144	C₁₁×C₄⋊C₄	—	2	1	no	—
145	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
146	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
147	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
148	C₁₁×C₂²⋊C₄	—	2	1	no	—
149	C₁₁×C₂²⋊C₄	—	2	2	no	—
150	C₁₁×C₂²⋊C₄	—	2	1	no	—
151	C₁₁×C₂²⋊C₄	—	2	2	no	—
152	C₁₁×C₂²⋊C₄	—	2	1	no	—
153	C₄²×C₁₁	—	2	1	no	—
154	C₄²×C₁₁	—	2	1	no	—
155	C₄²×C₁₁	—	2	1	no	—
156	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₁₁	#41	1	1	yes	characteristic
159	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
160	#2988	C₂×C₁₁	1	1	yes	characteristic, complemented
161	#2975	C₂×C₁₁	1	1	yes	characteristic, complemented
162	C₄×AGL(1,ℤ/8)	C₂×C₁₁	1	1	yes	characteristic
163	#1588	C₂×C₁₁	1	2	yes	complemented
164	#1586	C₂×C₁₁	1	2	yes	complemented
165	#1583	C₂×C₁₁	1	2	yes	complemented
166	#1581	C₂×C₁₁	1	2	yes	complemented
167	#1565	C₂×C₁₁	1	1	yes	characteristic, complemented
168	#1476	C₂×C₁₁	1	1	yes	characteristic, complemented
169	C₂×D₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
170	#1451	C₂×C₁₁	1	1	yes	characteristic, complemented
171	C₂³×C₁₁	—	2	1	no	—
172	C₂³×C₁₁	—	2	2	no	—
173	C₂³×C₁₁	—	4	2	no	—
174	C₂³×C₁₁	—	8	1	no	—
175	C₂³×C₁₁	—	8	1	no	—
176	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
177	Q₈×C₁₁	—	2	1	no	—
178	Q₈×C₁₁	C₂×M₁₆	1	2	yes	—
179	D₄×C₁₁	—	2	4	no	—
180	D₄×C₁₁	—	2	2	no	—
181	D₄×C₁₁	—	2	1	no	—
182	D₄×C₁₁	—	2	2	no	—
183	D₄×C₁₁	—	4	2	no	—
184	D₄×C₁₁	C₂×M₁₆	1	2	yes	—
185	C₂×C₄×C₁₁	—	2	1	no	—
186	C₂×C₄×C₁₁	—	2	1	no	—
187	C₂×C₄×C₁₁	—	2	1	no	—
188	C₂×C₄×C₁₁	—	2	4	no	—
189	C₂×C₄×C₁₁	—	2	1	no	—
190	C₂×C₄×C₁₁	—	2	1	no	—
191	C₂×C₄×C₁₁	—	2	2	no	—
192	C₂×C₄×C₁₁	—	4	1	no	—
193	C₂×C₄×C₁₁	—	4	1	no	—
194	C₂×C₄×C₁₁	—	4	2	no	—
195	C₂×C₄×C₁₁	—	4	2	no	—
196	C₂×C₄×C₁₁	—	4	1	no	—
197	C₂×C₄×C₁₁	—	8	1	no	—
198	C₂×C₄×C₁₁	—	8	2	no	—
199	C₂×C₄×C₁₁	—	8	1	no	—
200	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
204	C₂×C₄×C₁₁	#131	1	2	yes	—
205	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
208	C₈×C₁₁	—	2	2	no	—
209	C₈×C₁₁	—	2	2	no	—
210	C₈×C₁₁	—	2	2	no	—
211	C₈×C₁₁	—	2	2	no	—
212	C₈×C₁₁	—	2	2	no	—
213	C₈×C₁₁	—	4	1	no	—
214	C₈×C₁₁	—	4	2	no	—
215	C₈×C₁₁	—	4	1	no	—
216	C₈×C₁₁	—	4	1	no	—
217	C₂×AGL(1,ℤ/8)	C₄×C₁₁	1	1	yes	characteristic
218	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
219	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
220	C₈×Q₈	C₂²×C₁₁	1	2	yes	complemented
221	#442	C₄×C₁₁	1	2	yes	—
222	#440	C₄×C₁₁	1	2	yes	—
223	C₄×SD₁₆	C₂²×C₁₁	1	2	yes	—
224	C₄×D₈	C₂²×C₁₁	1	2	yes	—
225	#436	—	2	1	no	—
226	#436	—	2	1	no	—
227	#436	C₂²×C₁₁	1	2	yes	—
228	#436	C₂²×C₁₁	1	2	yes	—
229	C₈×D₄	—	2	2	no	—
230	C₈×D₄	C₂²×C₁₁	1	2	yes	complemented
231	#431	—	2	1	no	—
232	#431	C₂²×C₁₁	1	1	yes	characteristic
233	#431	C₂²×C₁₁	1	1	yes	characteristic
234	#428	C₄×C₁₁	1	1	yes	characteristic
235	C₂×C₄⋊C₈	—	2	1	no	—
236	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
237	#418	C₄×C₁₁	1	1	yes	characteristic
238	#417	C₄×C₁₁	1	1	yes	characteristic
239	#407	—	2	2	no	—
240	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
241	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
242	#335	C₂²×C₁₁	1	2	yes	complemented
243	#334	C₂²×C₁₁	1	2	yes	complemented
244	Q₈⋊C₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
245	Q₈⋊C₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
246	D₄⋊C₈	C₂²×C₁₁	1	2	yes	—
247	D₄⋊C₈	C₂²×C₁₁	1	2	yes	—
248	D₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
249	D₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
250	#322	C₂²×C₁₁	1	2	yes	complemented
251	#322	C₂²×C₁₁	1	2	yes	complemented
252	C₂²×C₁₁	—	2	1	no	—
253	C₂²×C₁₁	—	2	1	no	—
254	C₂²×C₁₁	—	2	2	no	—
255	C₂²×C₁₁	—	4	1	no	—
256	C₂²×C₁₁	—	4	1	no	—
257	C₂²×C₁₁	—	4	2	no	—
258	C₂²×C₁₁	—	4	2	no	—
259	C₂²×C₁₁	—	4	2	no	—
260	C₂²×C₁₁	—	8	4	no	—
261	C₂²×C₁₁	#435	1	2	yes	—
262	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
263	C₄×C₁₁	—	2	2	no	—
264	C₄×C₁₁	—	2	1	no	—
265	C₄×C₁₁	—	2	1	no	—
266	C₄×C₁₁	—	2	1	no	—
267	C₄×C₁₁	—	4	1	no	—
268	C₄×C₁₁	—	4	2	no	—
269	C₄×C₁₁	—	4	1	no	—
270	C₄×C₁₁	#435	1	2	yes	—
271	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
272	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
273	C₄×C₁₁	#576	1	1	yes	characteristic
274	C₄×C₁₁	#577	1	1	yes	characteristic
275	C₂×#41	C₂×C₄×C₁₁	1	1	yes	characteristic
276	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
277	C₂³×C₄	—	2	1	no	—
278	AGL(1,ℤ/8)	—	2	4	no	—
279	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
280	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
284	C₂×M₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
285	C₂²×C₈	—	2	1	no	—
286	C₂²×C₈	—	2	1	no	—
287	C₂²×C₈	—	2	2	no	—
288	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
289	C₄×Q₈	C₂³×C₁₁	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
295	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
296	C₄×D₄	C₂³×C₁₁	1	2	yes	—
297	C₄×D₄	C₂³×C₁₁	1	1	yes	characteristic
298	#117	—	2	1	no	—
299	#117	C₂×C₄×C₁₁	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
304	#107	C₂×C₄×C₁₁	1	2	yes	—
305	#106	C₂×C₄×C₁₁	1	2	yes	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
309	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
310	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
311	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
312	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
313	#103	C₂×C₄×C₁₁	1	2	yes	—
314	#102	C₂×C₄×C₁₁	1	2	yes	—
315	#102	C₂×C₄×C₁₁	1	2	yes	—
316	#102	C₂×C₄×C₁₁	1	2	yes	—
317	C₂²⋊C₈	—	2	1	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	C₂²⋊C₈	—	2	2	no	—
321	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
322	#97	C₂×C₄×C₁₁	1	2	yes	—
323	C₄×C₈	—	2	2	no	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	2	1	no	—
326	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
327	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
328	C₄×C₈	C₂³×C₁₁	1	2	yes	—
329	C₄×C₈	C₂³×C₁₁	1	2	yes	—
330	C₂×C₁₁	—	2	2	no	—
331	C₂×C₁₁	—	4	2	no	—
332	C₂×C₁₁	—	8	2	no	—
333	C₂×C₁₁	C₂×#435	1	1	yes	characteristic
334	C₂×C₁₁	#2946	1	1	yes	characteristic
335	C₂×C₁₁	#2956	1	1	yes	characteristic
336	C₂⁴	—	2	1	no	—
337	#41	—	2	2	no	—
338	#41	C₁₁×M₁₆	1	4	yes	complemented
339	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
345	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	8	1	no	—
353	C₂²×C₄	—	8	1	no	—
354	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
356	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
357	SD₁₆	—	2	4	no	—
358	D₈	—	2	4	no	—
359	M₁₆	—	2	2	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	8	2	no	—
362	M₁₆	—	8	2	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	—	8	2	no	—
370	C₂×C₈	—	8	1	no	—
371	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
372	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
373	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
374	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
379	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
380	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
390	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
391	C₄²	C₁₁×#41	1	1	yes	characteristic
392	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
393	C₁₁	#17875	1	1	yes	characteristic, direct product factor, Sylow
394	C₂³	—	2	1	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	8	1	no	—
398	C₂³	—	8	1	no	—
399	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
400	Q₈	—	2	1	no	—
401	Q₈	C₂×C₁₁×M₁₆	1	2	yes	—
402	D₄	—	2	4	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	1	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	2	no	—
407	D₄	C₂×C₁₁×M₁₆	1	2	yes	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	8	1	no	—
421	C₂×C₄	—	8	2	no	—
422	C₂×C₄	—	8	1	no	—
423	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
424	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
425	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
426	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
427	C₂×C₄	C₁₁×#131	1	2	yes	—
428	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
430	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	2	no	—
438	C₈	—	4	1	no	—
439	C₈	—	4	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	8	4	no	—
449	C₂²	C₁₁×#435	1	2	yes	—
450	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
451	C₄	—	2	2	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	C₁₁×#435	1	2	yes	—
459	C₄	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
460	C₄	C₂×C₁₁×#131	1	1	yes	characteristic
461	C₄	C₁₁×#576	1	1	yes	characteristic
462	C₄	C₁₁×#577	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	4	2	no	—
465	C₂	—	8	2	no	—
466	C₂	C₂×C₁₁×#435	1	1	yes	characteristic
467	C₂	C₁₁×#2946	1	1	yes	characteristic
468	C₂	C₁₁×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₄²	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×AGL(1,ℤ/8)	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₁₁×#431 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₁×#2988	C₂	semidirect
2. C₁₁×#2975	C₂	semidirect
4. C₁₁×#1588	C₂	semidirect
5. C₁₁×#1586	C₂	semidirect
6. C₁₁×#1583	C₂	semidirect
7. C₁₁×#1581	C₂	semidirect
8. C₁₁×#1565	C₂	semidirect
9. C₁₁×#1476	C₂	semidirect
10. C₂×C₁₁×D₄⋊C₈	C₂	semidirect
11. C₁₁×#1451	C₂	semidirect
15. C₈×Q₈×C₁₁	C₂²	semidirect
25. C₈×D₄×C₁₁	C₂²	semidirect
37. C₁₁×#335	C₂²	semidirect
38. C₁₁×#334	C₂²	semidirect
39. C₁₁×Q₈⋊C₈	C₂²	semidirect
40. C₁₁×Q₈⋊C₈	C₂²	semidirect
43. C₁₁×D₄⋊C₈	C₂²	semidirect
44. C₁₁×D₄⋊C₈	C₂²	semidirect
45. C₁₁×#322	C₂²	semidirect
46. C₁₁×#322	C₂²	semidirect
102. #17875	C₁₁	direct (N × H)
105. C₁₁×#41	M₁₆	semidirect
160. #2988	C₂×C₁₁	semidirect
161. #2975	C₂×C₁₁	semidirect
163. #1588	C₂×C₁₁	semidirect
164. #1586	C₂×C₁₁	semidirect
165. #1583	C₂×C₁₁	semidirect
166. #1581	C₂×C₁₁	semidirect
167. #1565	C₂×C₁₁	semidirect
168. #1476	C₂×C₁₁	semidirect
169. C₂×D₄⋊C₈	C₂×C₁₁	semidirect
170. #1451	C₂×C₁₁	semidirect
220. C₈×Q₈	C₂²×C₁₁	semidirect
230. C₈×D₄	C₂²×C₁₁	semidirect
242. #335	C₂²×C₁₁	semidirect
243. #334	C₂²×C₁₁	semidirect
244. Q₈⋊C₈	C₂²×C₁₁	semidirect
245. Q₈⋊C₈	C₂²×C₁₁	semidirect
248. D₄⋊C₈	C₂²×C₁₁	semidirect
249. D₄⋊C₈	C₂²×C₁₁	semidirect
250. #322	C₂²×C₁₁	semidirect
251. #322	C₂²×C₁₁	semidirect
338. #41	C₁₁×M₁₆	semidirect
393. C₁₁	#17875	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁×#2988	2
C₁₁×#2975	2
C₄×C₁₁×AGL(1,ℤ/8)	2
C₁₁×#1588	2
C₁₁×#1586	2
C₁₁×#1583	2
C₁₁×#1581	2
C₁₁×#1565	2
C₁₁×#1476	2
C₂×C₁₁×D₄⋊C₈	2
C₁₁×#1451	2
#17875	11

Subgroups — C11×#17875 #14595068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#17875 #14595068